DIVISION
OF NATURAL SCIENCE
NATS 1750 "The Earth and Its
Atmosphere"
Assignment #1
Distributed on the web site Sunday
23rd September, 2012
Due in your Tutorial #5 on Tuesday
16th or Thursday 18th October, 2012
NOTE: You must make and keep a photocopy of your
submitted assignment.
NOTE
ALSO: Marks will be deducted if you do not explain your answers or do not
show all relevant steps in your calculations
You
may discuss your assignment in groups but then you must go and do it on your own
i.e., submissions
with the same numerical errors or identical layouts, etc., will be carefully scrutinized by the markers for illegal
collaboration.
SOME INFO YOU MAY NEED:
Stefan-Boltzmann's Law is E
(watt m-2) = 5.7 x 10-8 (watt m-2 K-4) x T4
(K)
Wein's Displacement Law
is lmax (mm) x T (K) = 3000 (mm K)
p = 3.14; the
surface area of a sphere is 4pR2 ; 1 watt = 1 Joule
s-1
1. (This question deals with
increasing CO2 levels and the threat of global warming)
In 1900 the CO2 concentration in air was 0.030 %. In 2000 it was 0.036%.
(a) By how much has the CO2 concentration changed in parts
per million (ppm) over the last 100 years?
(b) Estimated by how much it has been increasing in terms of ppm per year.
(c) In 1999 the CO2 concentration was 355 ppm. Is this consistent with your answer to (b)
and what does it tell us about the way the CO2 is increasing?
2. (This question deals with how pressure decreases with height)
The surface pressure is 1000 mb and pressure
decreases with height.
(a) If the pressure halving height is 6 km what is the pressure in millibars at 60 km above the surface? Express your answer in scientific notation
with 3 numbers in the digit part, i.e. ?.?? x 10?
(b) What is the pressure at 60 km in millibars
to the nearest mb?
(c) Is it therefore true to say
that the pressure deceases by about a factor of 10 for every 15 km we go
up? Explain your answer.
3. (This question deals with radiation from the Sun)
If the Sun's surface has a
radius of R=700,000 km and its radiation peaks at a wavelength of lmax = 0.53 mm calculate,
using Wien's Displacement Law and the Stefan-Boltzmann Law, the total amount of
energy it emits in units of watts.
4. (This question deals with solar insolation)
(a) The attached contour
plot (Fig 1 below) shows how the 'insolation' , i.e.
the amount of solar radiation measured in units of energy metre-2 received at the
top of the atmosphere in a 24 hour period, varies with latitude and time of
year.
(i) Sketch a graph
with "insolation" as the vertical y-axis and "month" as the
horizontal x-axis showing how the insolation varies throughout the year for the
equator (i.e., 0), and for latitudes of 30, 45 and 90 North. Use the same graph but different colours or
types of lines to distinguish the curves for the different latitudes.
(ii) What are the
yearly maximum and minimum values of the insolation for each of the latitudes
you have plotted?
(iii) How does
the difference between yearly maximum and yearly minimum insolation vary with
latitude?
(iv)
Where and when does the maximum insolation occur?
N.B. You do not need to plot a
point on your graph for every month - you can simply sketch the curves by
finding when the insolation had some specific value.
(b) Now look at the global map (Fig 2 below)
showing the variation of solar radiation over the year at the surface.
(i) Why does more
energy reach the surface over the
(ii) Why is there so little energy (relatively
speaking) at the surface over
(iii) You saw in
part (a) above that at the top of the Earth's atmosphere there was more
insolation at the pole during the summer solstice than at the equator. Yet this
global map shows that over one year much less energy is received at the poles -
give 2 reasons for this.
Figure 1.
Figure 2.